2012/12/31 by I. Heckenberger, Andreas Lochmann, A. Lochmann +2 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Conjecture #Factorization #Geometric and Algebraic Topology #Hilbert–Poincaré series #Indecomposable module #Mathematics #Pure mathematics #math.CO #math.QA #msc:16T05 #msc:20F36 #msc:68Q80
paper · pdf · doi:10.1090/s0002-9947-2015-06231-x
published as Trans. Amer. Math. Soc. 367 (2015), no. 9, 6315-6356 · 46 pages, 20 figures. We improved significantly the text by adding more definitions and more explanations. Accepted for publication in Transactions of the American Mathematical Society
arxiv created 2013/06/30 · openalex publication_date 2015/01/30 · arxiv updated 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.